(A) 1. Field of the Invention
The invention relates to a discrete transversal filter with a given cut-off frequency for processing input samples x(n) and for producing output samples y(n) which occur with a predetermined output sampling frequency f.sub.s which is equal to an integral multiple of said cut-off frequency, which discrete filter has a predetermined lowpass transfer characteristic which is related to the transfer characteristic of a predetermined lowpass filter having an impulse response h.sub.1 (i), said discrete filter comprising:
AN INPUT FOR RECEIVING SAID INPUT SAMPLES X(N);
A TAPPED DELAY LINE FOR STORING AND PRODUCING N input samples x(n) wherein the delay time of the delay line situated between each two successive tapes is equal to 1/f.sub.s ;
FIRST STORAGE MEANS FOR STORING AND PRODUCING FILTER COEFFICIENTS H.sub.1 (I);
FIRST MULTIPLYING MEANS FOR MULTIPLYING EACH OF THE INPUT SAMPLES PRODUCED AT THE SAID TAPS WITH A CORRESPONDING FILTER COEFFICIENT FOR GENERATING MODIFIED INPUT SAMPLES Z(N, I) = H.sub.1 (I) .times. (N - I);
FIRST ADDER MEANS;
FIRST MEANS FOR COUPLING THE INPUT CIRCUIT OF THE FIRST ADDER MEANS TO THE OUTPUT CIRCUIT OF THE FIRST MULTIPLYING MEANS.
(A) 2. Description of the Prior Art
Discrete filters may be divided into two classes (see chapter D, reference 1), namely:
1. Sampled-data filters. The input signal samples x(n) occurring in these filters as well as the output signal samples y(n) are not amplitude-discrete. In such a filter the delay line is formed by a shift register for non-amplitude discrete samples. This shift register may be constructed by means of, for example, "charge coupled devices" (C.C.D's). PA0 2. Digital filters. The input samples x(n) occurring in these filters and the output signal sample y(n) as well as the filter coefficients are amplitude-discrete and are available in the form of digital numbers with a given number of bits. Herein the delay line is again constituted by a shift register, however, each of the shift register elements is now arranged for storing and releasing a digital number x(n). It should be noted that the representation of these digital numbers (see also reference 1) is of no importance for the present invention. PA0 means for producing a first, a second and a third set of coefficients {a(1, r)}, {a(2, r)}, {a(3, r)} of which first set of coefficients {a(1, r)} the elements a(1, r) are given by: a(1, r) = 1, PA0 of which second set of coefficients {a(2, r)} the elements a(2, r) are given by: a(2, r) = cos(2.pi.rf.sub.g /f.sub.s), of which third set of coefficients {a(3, r)} the elements a(3, r) are given by a (3, r) = sin(2.pi.rf.sub.g /f.sub.s); PA0 means for selectively applying the first, the second and the third set of coefficients {a(q, r)} to said multiplying means; PA0 third coupling means for coupling the output circuit of the second multiplying means to the input circuit of the first adder means. PA0 means for supplying a first coefficient .alpha. = +1 and a second coefficient .beta. = -1; PA0 third multiplying means to which sum value P(n, m) where ##EQU3## are applied; means for selectively applying the coefficients .alpha. and .beta. to the third multiplying means for generating modified sum values S(n, m); PA0 means for adding sum values and modified sum values together for generating values R(n, r) which are given by: EQU R(n, r) = P(n, r) + S(n, r+f.sub.s /(2f.sub.g) ) (9a) PA0 means for applying the values R(n, r) to said second multiplying means for generating products EQU Q(q,n,r) = a(q,r).multidot.R(n,r) (10)
A discrete transversal filter is a device which is used for producing output samples y(n) which are each related to the sum of a plurality of N algebraic products which in turn are each related to N input samples x(n), the relation between y(n) and x(n) being given by the equation: ##EQU1## Herein a(i) represent constant coefficients which are a function of the transfer characteristic of the desired filter.
The expression (1) which an output signal sample y(n) must satisfy is the same for the above-mentioned kinds of discrete transversal filters. Consequently, what follows herebelow applies to both sampled-data filters and to digital filters and the invention will be further explained with reference to a digital filter.
As has already been observed the filter coefficients a(i) are a function of the transfer characteristic of the desired filter. For a lowpass filter with an impulse response h.sub.1 (i) therefore: EQU a(i) = h.sub.1 (i) (2)
In analog signal processing a second lowpass filter having a cut-off frequency 2f.sub.g can be derived from a given lowpass filter having a cut-off frequency f.sub.g and an impulse response h.sub.1 (t). If the impulse response of this second lowpass filter is represented by h.sub.F (t) then (see reference 2) EQU h.sub.F (t) = h.sub.1 (t) cos2.pi.f.sub.g t (3)
In complete agreement herewith it applies that a lowpass discrete filter having a cut-off frequency 2f.sub.g can be derived from a lowpass discrete filter having a cut-off frequency f.sub.g and an impulse response h.sub.1 (i). If h.sub.F (i) represents the impulse response of the lowpass discrete filter having a cut-off frequency 2f.sub.g, then it holds, for example, that: EQU h.sub.F (i) = h.sub.1 (i)cos(2.pi.if.sub.g /f.sub.s) (4)
The filter coefficients of this filter will be designated by a.sub.F (i) and these coefficients can again be given by the equation: EQU a.sub.F (i) = h.sub.F (i) (5)
The filter having the impulse response defined in expression (4) will hereinafter be referred to as in-phase filter.
In, for example, single sideband and vestigial side-band modulation systems (see, for example, reference 3) not only a filter having the impulse response defined in expression (4) but also a filter having a pulse response of the form: EQU h.sub.Q (i) = h.sub.1 (i)sin(2.pi.if.sub.g /f.sub.s) (6)
is used. The filter coefficients of this filter will be indicated by a.sub.Q (i) and are again given by the expression EQU a.sub.Q (i)= h.sub.Q (i) (7)
The filter having the impulse response defined in expression (6) will hereinafter be referred to as a quadrature filter.
Depending on the type of modulation system for data signals and depending on the bit rate of these data signals use will be made in such a modulation system of one of more of said lowpass filters with cut-off frequency f.sub.g or one or more of the in-phase filters or each time an in-phase filter will be used together with a quadrature filter. This means that for each type of modulation system the relevant filters must be available. The modulation systems in which the in-phase filters are used and in which data signals are processed which occur at a bit rate of f.sub.s are furthermore often completed with the above-mentioned lowpass filters with cut-off frequency f.sub.g which are suitable for processing data signals which are applied thereto with a bit rate f.sub.s /2.
The use of the discrete in-phase and quadrature filter in said modulation system results for example in the application of two discrete filters which operate fully independently, the coefficients a.sub.F (i) being used in the in-phase filter and the coefficients a.sub.Q (i) in the quadrature filter. A second possibility which results in a considerably simpler discrete filter is to first modify each of the input samples x(n-i) with a relevant coefficient h.sub.1 (i) of the lowpass filter having the cut-off frequency f.sub.g to produce modified input samples z(n,i) = h.sub.1 (i)x(n-i) and to multiply thereafter each of these modified input samples z(n,i) where (i = 0, 1, 2, . . . N-1) by either a relevant coefficient cos(2.pi.if.sub.g /f.sub.s) or by a coefficient sin(2.pi.if.sub.g /f.sub.s) for realizing the in-phase or quadrature filter respectively.